Basic Math Examples

$\frac{j \cdot 1}{4} - 1 \frac{2}{3} = 3 \frac{7}{12}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{j \cdot 1}{4} - 1 \frac{2}{3}$ .

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Step 1.1.1

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{j \cdot 1}{4} - (1 + \frac{2}{3}) = 3 \frac{7}{12}$

Step 1.1.1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{j \cdot 1}{4} - (\frac{3}{3} + \frac{2}{3}) = 3 \frac{7}{12}$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{j \cdot 1}{4} - \frac{3 + 2}{3} = 3 \frac{7}{12}$

Step 1.1.1.2.3

Add $3$ and $2$ .

$\frac{j \cdot 1}{4} - \frac{5}{3} = 3 \frac{7}{12}$

Step 1.1.2

Multiply $j$ by $1$ .

$\frac{j}{4} - \frac{5}{3} = 3 \frac{7}{12}$

Step 2

Simplify the right side.

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Step 2.1

Convert $3 \frac{7}{12}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{j}{4} - \frac{5}{3} = 3 + \frac{7}{12}$

Step 2.1.2

Add $3$ and $\frac{7}{12}$ .

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Step 2.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{j}{4} - \frac{5}{3} = 3 \cdot \frac{12}{12} + \frac{7}{12}$

Step 2.1.2.2

Combine $3$ and $\frac{12}{12}$ .

$\frac{j}{4} - \frac{5}{3} = \frac{3 \cdot 12}{12} + \frac{7}{12}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{j}{4} - \frac{5}{3} = \frac{3 \cdot 12 + 7}{12}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $3$ by $12$ .

$\frac{j}{4} - \frac{5}{3} = \frac{36 + 7}{12}$

Step 2.1.2.4.2

Add $36$ and $7$ .

$\frac{j}{4} - \frac{5}{3} = \frac{43}{12}$

Step 3

Move all terms not containing $j$ to the right side of the equation.

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Step 3.1

Add $\frac{5}{3}$ to both sides of the equation.

$\frac{j}{4} = \frac{43}{12} + \frac{5}{3}$

Step 3.2

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{j}{4} = \frac{43}{12} + \frac{5}{3} \cdot \frac{4}{4}$

Step 3.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{5}{3}$ by $\frac{4}{4}$ .

$\frac{j}{4} = \frac{43}{12} + \frac{5 \cdot 4}{3 \cdot 4}$

Step 3.3.2

Multiply $3$ by $4$ .

$\frac{j}{4} = \frac{43}{12} + \frac{5 \cdot 4}{12}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{j}{4} = \frac{43 + 5 \cdot 4}{12}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $5$ by $4$ .

$\frac{j}{4} = \frac{43 + 20}{12}$

Step 3.5.2

Add $43$ and $20$ .

$\frac{j}{4} = \frac{63}{12}$

Step 3.6

Cancel the common factor of $63$ and $12$ .

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Step 3.6.1

Factor $3$ out of $63$ .

$\frac{j}{4} = \frac{3 (21)}{12}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $3$ out of $12$ .

$\frac{j}{4} = \frac{3 \cdot 21}{3 \cdot 4}$

Step 3.6.2.2

Cancel the common factor.

$\frac{j}{4} = \frac{3 \cdot 21}{3 \cdot 4}$

Step 3.6.2.3

Rewrite the expression.

$\frac{j}{4} = \frac{21}{4}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$j = 21$